Suburban furnace won't kick on the 2nd time

The most common part that fails when this type problem happens is a BAD Ignitor control module. The memory on the board fails. This is when it fails to start the 2nd time automatically and IF you turn the tstat OFF and back on the furnace then runs and lights. Doug

"Kick on" is far too generic of terminology. Describe in detail.

What if anything was done or worked on just prior to the problem starting.

Yes, please clarify if the blower does not even come on when the temp drops to where you expect the furnace to cycle back on.

If the blower comes on but there is no ignition of the gas that is one (or more) thing(s), but if it does not, then it could still be a thermostat issue with the "swing" temp spread

What exact model thermostat is the Emerson? Some thermostats do not work with RV furnaces. (Some of those can be wired funny to make them work)

On the first heat cycle, does the furnace run long enough to bring the temperature up to the thermostat setting before shutting off? Then after when the temp drops low enough for heat, does the fan come on, or not at all?

When you turn off your thermostat and back on it sounds more like you are resetting the safety shut-off at the burner control. Most likely you have a flame problem or flame sensing problem. If your flame is a nice blue then it is a flame sensing issue. Try cleaning the flame sensor if you are comfortable doing so.

Want to verify T-Stat isn't the problem? Run your camper to 72 deg.- let it cool back to 60 deg.- move T-Sta to 62 deg.- turn T-Stat off and back on. If the burner starts then you just proved your T-Stat is ok and the burner was off on safety.

Furnace once reaching the desired temp [72] will kick off and will only restart if I turn OFF and back on to a desired temp. Temp fell to 60deg which should have kicked the furnace back on.
I am plugged in to a 50amp pedestal here at the CG and my converter is working perfectly.
I replaced the thermostat [Suburban] because it did the same as now and someone told me it was my thermostat, so I bought a new Emerson at the RV dealership.
I don't know what the swing should be, but I am assuming that a temp of 60deg should have made it kick back in.

Does the "kick on" mean the blower starts but no heat comes on after that, or the blower does not even start?

Is there enough 12v voltage to run it after it ran a while the first time?

Why did you replace the thermostat--same thing before that? What thermostat did you use as a replacement?

The "swing" between set room temp and what the thermostat lets it get down to could be excessive with the wrong thermostat, so you might not be that low for the furnace to come on yet.